Author

Erik Bates

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Open access Jun 2025

Permutation invariance in last-passage percolation and the distribution of the Busemann process

In i.i.d. exponential last-passage percolation, we describe the joint distribution of Busemann functions, over all edges and over all directions, in terms of a joint last-passage problem in a finite inhomogeneous environment. More specifically, the Busemann increments within a $$k\times \ell $$ k × ℓ...

Erik Bates, Elnur Emrah, James B. Martin et al. · Probability theory and relat... · 2 citations

Preprint Aug 2026

Negative association of Busemann functions in exponential last-passage percolation

One hallmark of exactly solvable KPZ random growth models is product-form invariant measures. In the setting of exponential last-passage percolation (LPP), this corresponds to the independence of Busemann increments along any down-right path. However, this independence breaks down when multiple asymptotic directions ar...

Erik Bates, Xiao Shen · 0 citations